A train runs between stations on a straight track. Predict where it stops and how far it is displaced, then move the origin: every position changes, but the displacement does not.

PositionReference point

Play Train Track

Position: x = +700 m
Displacement: Δx = x_f − xᵢ

PLAY NOW · 02

Lift Trips: Distance or Displacement?

A lift stops at several floors, from the car park to the top. Predict the distance it travels and its displacement, then watch the trip log add every stretch while the displacement arrow only links start and finish.

DistanceDisplacement

Play Lift Trips

Distance: s = Σ|Δyᵢ|
Displacement: Δy = y_f − yᵢ

PLAY NOW · 03

Dog Walk: Read the Position Graph

A dog walks out from a bench, waits, and runs back. Read its position, displacement, and distance from the position–time graph, then watch the dog and the graph move together.

Position–time graphsDistance and displacement

Play Dog Walk

Position at a time: x(8 s) = 4 m
Displacement: Δx = x(t₂) − x(t₁)

PLAY NOW · 04

Speed & velocity

Catch a moving target or send a particle around a track. Discover why traveling farther does not always mean moving farther from the start.

Physics labPac-Man chase

Play the speed and velocity simulation

Average speed: s̄ = d / t
Average velocity: v̄ = Δr / t

PLAY NOW · 05

Graph Rider: Match the Velocity Graph

A cart must follow a target velocity–time graph. Read each slope, set the acceleration, and watch your trace land on the line, or drift away from it.

Acceleration as slopeVelocity–time graphs

Play Graph Rider

Acceleration is the slope: a = Δv ÷ Δt
Displacement is the area: Δx = area under v–t

PLAY NOW · 06

Galileo's Bells: Ring on the Beat

A ball rolls down a ramp, speeding up all the way. Place four bells so they ring on a steady beat, and hear why equal times do not mean equal distances.

Uniform accelerationDistance and time squared

Play Galileo's Bells

Distance from rest: x = ½·a·t²
Gaps on a steady beat: 1 : 3 : 5 : 7

PLAY NOW · 07

Stop on the Line: Brake Just in Time

A car approaches a red light. Predict where to brake so the bumper stops exactly on the line: on a dry road, on a wet road, or after a reaction delay.

DecelerationBraking distance

Play Stop on the Line

Braking distance: d = v₀² ÷ (2a)
Stopping time: t = v₀ ÷ a

PLAY NOW · 08

Drop Test: How Long to Fall?

Drop a ball from a balcony, from a tower, or on the Moon. Predict when it lands and how fast it hits, and find out whether a heavy ball falls faster than a light one.

Free fallAcceleration due to gravity

Play Drop Test

Fall from rest: h = ½·g·t²
Impact speed: v = √(2·g·h)

PLAY NOW · 09

Straight Up: Throw and Catch

Throw a ball straight up and catch it again. Predict how long it rises, how high it goes, and its acceleration at the top, where it stops for an instant.

Vertical throwAcceleration at the top

Play Straight Up

Time to the top: t = v₀ ÷ g
Maximum height: y_max = v₀² ÷ (2g)

PLAY NOW · 10

Reaction Ruler: Catch It!

A friend drops a ruler and you catch it. The mark where your fingers close gives your reaction time through d = ½·g·t². Predict the catches, then measure your own reaction.

Free fallReaction time

Play Reaction Ruler

Distance fallen: d = ½·g·t²
Reaction time: t = √(2d ÷ g)

PLAY NOW · 11

Lunar Lander: Eco-Mission

Guide a falling module onto a landing platform. Learn how opposing accelerations slow a descent, and try a fuel-saving landing on the Moon or Mars.

GravityAcceleration

Play Lunar Lander

Net acceleration: a = aₜ − g
Touchdown velocity: |v| ≤ 1.5 m/s

Measurement

2 games

PLAY NOW · 12

Unit Pipeline: Tank Fill Challenge

Convert litres, cubic centimetres, minutes, and hours with the factor-label method. Predict the fill time, then let the tank test your prediction.

Unit conversionSI units

Play Unit Pipeline

Fill time: t = V ÷ Q
Volume: 1 m³ = 1000 L

PLAY NOW · 13

Powers-of-Ten Probe

Follow a bacterium, a nerve signal, an airliner, and light itself. Convert SI prefixes, predict each travel time in scientific notation, and zoom the ruler across the scales.

SI prefixesScientific notation

Play Powers-of-Ten Probe

Travel time: t = d ÷ v
Micro: 1 μm = 10⁻⁶ m

Formulas

3 games

PLAY NOW · 14

Formula Balance: Do It to Both Sides

An equation is a balance. Multiply, divide, square, or take a root on both sides to get the unknown alone, then weigh it. Do something to one side only and watch the scale tip.

Rearranging formulasInverse operations

Play Formula Balance

Same on both sides: d ÷ v = v·t ÷ v
Isolated: t = d ÷ v

PLAY NOW · 15

Undo Machine: Run the Formula Backwards

Every formula is a machine: the unknown goes in, operations act on it, and the result comes out. Build the reverse machine, last step first, and send the known value back through it.

Inverse operationsOrder of operations

Play Undo Machine

Forward: t → × v → + x₀ → x
Backward: x → − x₀ → ÷ v → t

PLAY NOW · 16

Formula Test Drive: Which Rearrangement Works?

Four rearranged formulas, one right answer. Check the units, pick one, and watch a car drive with your value: it stops on the line, or it does not.

Rearranging formulasChecking units

Play Formula Test Drive

Units must match: [d ÷ v] = m ÷ (m/s) = s
Then test it: t = d ÷ v

Vectors

3 games

PLAY NOW · 17

River Crossing: Beat the Current

Steer a boat across a flowing river. Discover why aiming straight across lands you downstream, and find the heading that cancels the current.

Vector additionRelative velocity

Play River Crossing

Ground velocity: v = v_b + v_w
Straight across: s · sin θ = u

PLAY NOW · 18

Orienteering Walk: Find the Shortcut

Follow a compass route leg by leg. Watch the distance walked keep growing while the displacement can shrink back to zero, then predict the shortcut.

Scalars and vectorsDisplacement

Play Orienteering Walk

Displacement: Δr = r₁ + r₂ + …
Distance: s = Σ|rᵢ| ≥ |Δr|

PLAY NOW · 19

Force Table: Balance the Ring

Balance a ring pulled by strings at different angles. Discover why 3 N and 4 N need exactly 5 N to cancel, and why only the vector sum matters.

Vector sumEquilibrium

Play Force Table

Equilibrium: ΣF = 0
Sizes: |F₁ + F₂| ≤ |F₁| + |F₂|

Trigonometry

3 games

PLAY NOW · 20

Loading Ramp: Find the Missing Side

A winch pulls boxes up a ramp onto a platform. Name the opposite, adjacent, and hypotenuse, pick the right ratio, and calculate the side that makes the ramp fit.

Right trianglesSine, cosine, tangent

Play Loading Ramp

Height of the ramp: h = L · sin θ
Ratios: tan θ = opp ÷ adj

PLAY NOW · 21

Lighthouse Rescue: Aim with Angles

A rescue drone flies in a straight line from the lighthouse to a ship. Find the angle of depression or elevation with the inverse functions, or the distance from a known angle.

Inverse functionsElevation and depression

Play Lighthouse Rescue

Angle of depression: tan α = H ÷ D
Back to the angle: α = tan⁻¹(H ÷ D)

PLAY NOW · 22

Ferris Wheel: Sine and Cosine on a Circle

A cabin rides a Ferris wheel past 90°, 180°, and beyond. Predict its coordinates with cosine and sine, find the signs in each quadrant, and earn a bonus for exact values.

Unit circleSpecial angles

Play Ferris Wheel

Cabin position: (R · cos θ, R · sin θ)
Special angle: sin 30° = 1/2

Projectile motion

3 games

PLAY NOW · 23

Air Drop: Hit the Target from the Plane

A plane in level flight drops a supply crate. Predict how long it falls, where to release it, and how fast it lands, and watch it stay right below the plane all the way down.

Horizontal launchIndependent motions

Play Air Drop

Fall time: t = √(2h ÷ g)
Distance forward: d = v·t

PLAY NOW · 24

Two Shadows: One Throw, Two Simple Motions

Throw a ball at an angle and follow its two shadows: the floor shadow glides at constant speed, the wall shadow rises, stops, and falls. Predict the components, the top, and the landing.

Velocity componentsAngled launch

Play Two Shadows

Floor shadow: x = v₀·cos θ·t
Wall shadow: y = v₀·sin θ·t − ½·g·t²

PLAY NOW · 25

Range Cannon: Find the Angle

Fire a cannon at different angles. Predict the range, find the second angle that lands in the same spot, and work out the angle or speed that hits a target.

RangeLaunch angle

Play Range Cannon

Range: R = v₀²·sin(2θ) ÷ g
Same range: θ₂ = 90° − θ

Circular motion

3 games

PLAY NOW · 26

Carousel: Time the Lap

Ride a carousel that turns at a steady rate. Predict the period, the angular velocity, the speed of a horse, and the angle it turns through.

Uniform circular motionAngular velocity

Play Carousel

Angular velocity: ω = 2π ÷ T
Speed: v = ω·r

PLAY NOW · 27

Spin Station: Artificial Gravity

Spin a ring-shaped space station. Predict the centripetal acceleration of the astronaut on its rim, and find the spin rate, period, or radius that recreates Earth or Moon gravity.

Centripetal accelerationArtificial gravity

Play Spin Station

Centripetal acceleration: a = v² ÷ r = ω²·r
Period: T = 2π·√(r ÷ a)

PLAY NOW · 28

Curve Ahead: Grip and Speed

Drive a car into a flat curve. Predict the centripetal force the tyres must supply, the top speed on dry and wet roads, and the tightest curve. Too little grip and the car runs wide.

Centripetal forceFriction

Play Curve Ahead

Centripetal force: F = m·v² ÷ r
Top speed: v = √(μ·g·r)

Gravitation

3 games

PLAY NOW · 29

Planet Scale: Gravity on Other Worlds

Weigh an astronaut and drop a ball on the Moon, Mars, and a super-Earth. Predict g = G·M ÷ R², the weight W = m·g, and the fall time, and find out what happens to the mass.

Surface gravityWeight and mass

Play Planet Scale

Surface gravity: g = G·M ÷ R²
Weight: W = m·g

PLAY NOW · 30

Satellite Launch: Universal Gravitation

Launch a satellite above Earth. Use F = G·M·m ÷ r² to predict the pull, see why twice as far means a quarter of the pull, and find the speed for a circular orbit and the geostationary radius.

Universal gravitationOrbits

Play Satellite Launch

Universal gravitation: F = G·M·m ÷ r²
Circular orbit: v = √(G·M ÷ r)

PLAY NOW · 31

Kepler's Clock: Periods and Distances

Time the Moon, Jupiter's moons, Earth, and Mars. Use Kepler's third law, T² = 4π²·r³ ÷ (G·M), to predict periods, weigh Jupiter, and find how far Mars is from the Sun.

Kepler's third lawOrbital period

Play Kepler's Clock

Kepler's third law: T² = 4π²·r³ ÷ (G·M)
Mass from an orbit: M = 4π²·r³ ÷ (G·T²)

Statics

3 games

PLAY NOW · 32

Hanging Sign: Balance the Cables

Hang a 20 kg sign from one or two cables. Use ΣF = 0 to find each tension, discover why flat cables pull much harder, and find the shallowest angle a cable can take.

Force equilibriumTension

Play Hanging Sign

Up and down: Σ T·sin θ = W
Across: T₁·cos θ₁ = T₂·cos θ₂

PLAY NOW · 33

Seesaw: Balance the Torques

Balance a seesaw with children of different masses. Use torque, weight × distance, to place them, include the plank's own weight, and find the force that lifts a wheelbarrow.

TorqueRotational equilibrium

Play Seesaw

Balance: ΣM = 0
Torque: M = m·g·d

PLAY NOW · 34

Plank Bridge: Share the Load

Load a plank resting on two supports. Use ΣF = 0 and ΣM = 0 to find each support's reaction, include the plank's weight, and find where a support cracks or the plank tips.

Static equilibriumSupport reactions

Play Plank Bridge

Forces: R_A + R_B = W + w
Moments about A: R_B·L = W·x + w·x_c

Torque and rotation

5 games

PLAY NOW · 35

Stuck Bolt: Turn the Wrench

Loosen a rusted bolt with a wrench. Find the push it needs, see why the angle matters, lengthen the lever with a pipe, and share the work between two hands.

TorqueLever arm

Play Stuck Bolt

Torque: τ = F·r·sin φ
Lever arm: d = r·sin φ

PLAY NOW · 36

Forklift: Don't Tip Over

Lift pallets without tipping a forklift. Compare the load's moment with the truck's about the front wheels, add a counterweight, and read a capacity plate.

TippingMoments

Play Forklift

Tipping limit: m·x ≤ M·b
Rear wheels: R_r·L = M·g·b − m·g·x

PLAY NOW · 37

Flywheel Race: Spin Up on Pace

Spin flywheels up with a pulled cord. Use τ = I·α to time a spin-up, set the pull, place masses on the spokes, beat bearing friction, and hold a steady speed.

Angular accelerationMoment of inertia

Play Flywheel Race

Rotation law: τ_net = I·α
Moment of inertia: I = I₀ + Σ m·r²

PLAY NOW · 38

Lever Lab: Three Classes of Lever

Try all three classes of lever: a crowbar, a nutcracker, and your own forearm. Find the effort, place the fulcrum, and see why some levers multiply force and others cost it.

LeversMechanical advantage

Play Lever Lab

Law of the lever: F·d_e = W·d_l
Mechanical advantage: MA = d_e ÷ d_l

PLAY NOW · 39

Force for Distance: What a Lever Trades

Levers don't give work for free. Watch a crowbar trade force for distance and a forearm trade force for speed, and check that the work in equals the work out.

LeversWork

Play Force for Distance

Distances: s_l ÷ s_e = d_l ÷ d_e
Work in = work out: F·s_e = W·s_l

Centre of mass

3 games

PLAY NOW · 40

Balance Point: Find the Centre of Mass

Balance a loaded beam on a narrow support. Weight each position by its mass to find the centre of mass, include the beam's own weight, and place or choose a mass to move the balance point.

Centre of massBalance

Play Balance Point

Centre of mass: x_cm = Σm·x ÷ Σm
Level when: |x_cm − x_s| ≤ 1 cm

PLAY NOW · 41

Hanging Mobile: Level Every Rod

Build a mobile that hangs level. Find the balance point of each rod, work from the bottom up, and treat a whole lower mobile as a single mass hanging at the end of a rod.

Centre of massComposite objects

Play Hanging Mobile

Knot: x_k = Σm·x ÷ Σm
Lower mobile: M = m₁ + m₂ + …

PLAY NOW · 42

Block Tower: Reach Past the Edge

Stack blocks out past a table's edge without toppling. Keep the centre of mass of every part of the stack over the block below it, add a counterweight, and find out how far a stack can lean.

Centre of massToppling

Play Block Tower

Stays put while: x_cm ≤ x_edge
Three-block reach: L·(1/2 + 1/4 + 1/6)

Fluids

9 games

PLAY NOW · 43

Density Detective: Archimedes' Crown

Lower a block, a crown, and a stone into a measuring cylinder. Read the volume from the rising water, work out ρ = m ÷ V, and find out whether the king's crown is pure gold.

DensityArchimedes

Play Density Detective

Density: ρ = m ÷ V
Volume from water: V = V₁ − V₀

PLAY NOW · 44

Barge Load: Archimedes' Principle

A floating barge sinks until the water it pushes aside weighs as much as it does. Predict its waterline, load it to the brim without flooding, and find out why steel boats float.

BuoyancyFloating

Play Barge Load

Buoyancy: F_b = ρ·g·V
Draft: d = M ÷ (ρ·A)

PLAY NOW · 45

Deep Dive: Pressure under Water

Every 10 m of seawater adds about one atmosphere. Read a submarine's gauge, find the deepest dive its hull can take, and see why fresh water lets it go a little deeper.

PressureDepth

Play Deep Dive

Pressure: p = p₀ + ρ·g·h
Force on a surface: F = Δp·A

PLAY NOW · 46

Weighed Under Water: What the Scale Loses

Hang a stone from a spring scale and lower it into a can full to the spout. The scale loses exactly the weight of the water that spills out. Use it to find volumes, densities, and depths, in water and in oil.

Archimedes' principleBuoyancy

Play Weighed Under Water

Buoyancy: F_b = ρ·g·V
Scale reading: R = W − F_b

PLAY NOW · 47

Balloon Lift: Archimedes in the Air

Air pushes up too, with the weight of the air a balloon pushes aside. Count party balloons for a toy, load and heat a hot-air balloon, fly from a mountain, and lift a person on helium.

Archimedes' principleBuoyancy in air

Play Balloon Lift

Lift: F = (ρ_air − ρ_in)·g·V
Hot air: ρ·T = const

PLAY NOW · 48

Torricelli's Tube: Weighing the Air

Turn a tube of mercury upside down and watch the air hold up a 760 mm column. Find the air pressure on a mountain, and why a suction pump can't lift water more than about 10 m.

Air pressureBarometer

Play Torricelli's Tube

Barometer: p = ρ·g·h
Column height: h = p ÷ (ρ·g)

PLAY NOW · 49

Magdeburg Hemispheres: the Air Holds Tight

In 1654 two teams of horses could not pull apart two metal halves held together only by the air. Find the force, F = Δp·π·r², count the horses, and see what a suction cup can hold.

Air pressureForce

Play Magdeburg Hemispheres

Force from pressure: F = (p_out − p_in)·A
Area: A = π·r²

PLAY NOW · 50

Hydraulic Lift: Pascal's Principle

Oil passes pressure on to every part of a lift, so a small push on a small piston lifts a car on a big one. Find the push, the piston sizes, and the long way the small piston has to travel.

Pascal's principleHydraulics

Play Hydraulic Lift

Same pressure: F₁ ÷ A₁ = F₂ ÷ A₂
Same volume: A₁·d₁ = A₂·d₂

PLAY NOW · 51

Pascal's Barrel: a Cupful Bursts a Lid

Pour a little water into a tall thin tube on a sealed barrel and the pressure reaches every wall. Find the height that pops the lid, see why the tube's width doesn't matter, and push a cork into a bottle.

Pascal's principlePressure

Play Pascal's Barrel

Extra pressure: Δp = ρ·g·h
Force on a surface: F = Δp·A

Fluids in motion

3 games

PLAY NOW · 52

Leaky Tank: How Far Does the Jet Go?

Water deeper in a tank spurts out faster: v = √(2·g·h). Predict a jet's speed and landing spot, fill a bucket, and find the two holes that land together and the hole that shoots farthest.

Bernoulli's principleTorricelli's law

Play Leaky Tank

Jet speed: v = √(2·g·h)
Landing distance: x = 2·√(h·y)

PLAY NOW · 53

Venturi Pipe: Faster Water, Lower Pressure

Where a pipe narrows, water speeds up and its pressure drops. Predict a nozzle's jet, the drop in a narrow pipe, the columns of a Venturi meter, the flow it measures, and a fountain's height.

Bernoulli's principleContinuity

Play Venturi Pipe

Continuity: A₁·v₁ = A₂·v₂
Bernoulli: Δp = ½·ρ·(v₂² − v₁²)

PLAY NOW · 54

Storm and Wing: Fast Air Pulls Up

Fast air has lower pressure. Predict the pull of a storm on a roof and the wind that tears it off, the lift on a wing, a plane's take-off speed, and the breath that raises a paper strip.

Bernoulli's principleLift

Play Storm and Wing

Pressure difference: Δp = ½·ρ·(v_over² − v_under²)
Lift: F = Δp·A

Oscillations

10 games

PLAY NOW · 55

Metronome Studio: Keep the Beat

The period is the time for one beat; the frequency is how many beats fit in a second. Turn tempos into periods and hertz into beats per minute, count beats, and find when two metronomes click together.

PeriodFrequency

Play Metronome Studio

Frequency: f = 1 ÷ T
Tempo: tempo = 60·f

PLAY NOW · 56

Harbour Buoy: How Big Is the Swing?

Amplitude is how far an oscillation swings from the middle, not from top to bottom. Read it off a harbour post, see the period stay the same on a bigger swell, and find distances, speeds, and energies.

AmplitudeSimple harmonic motion

Play Harbour Buoy

Amplitude: A = (y_max − y_min) ÷ 2
Top speed: v_max = 2π·A ÷ T

PLAY NOW · 57

Seismograph: Read the Shaking

A seismograph turns shaking into a wavy line. Read the period from the peak spacing and the paper speed, the frequency from the period, and the ground's tiny amplitude from the magnified trace.

Period and frequencyAmplitude

Play Seismograph

Period: T = d ÷ u
Amplitude: x = a ÷ M

PLAY NOW · 58

Pendulum Clock: Keep the Beat

A pendulum's period depends only on its length and on g: T = 2π·√(L ÷ g). Build a seconds pendulum, time a short one, double a period, swing one on the Moon, and try a heavier bob.

Simple harmonic motionPendulum

Play Pendulum Clock

Period: T = 2π·√(L ÷ g)
Seconds pendulum: L = g·(T ÷ 2π)²

PLAY NOW · 59

Wrecking Ball: Height Becomes Speed

A swinging ball trades height for speed and back: v = √(2·g·h). Find speeds at the bottom and partway down, the rope's pull, Galileo's peg, and the angle a given speed reaches.

PendulumEnergy conservation

Play Wrecking Ball

Drop: h = L·(1 − cos θ)
Speed: v = √(2·g·h)

PLAY NOW · 60

Big and Fading Swings: What the Formula Leaves Out

T = 2π·√(L ÷ g) is only exact for tiny swings, and real swings fade. Find a big swing's period, a clock's error, how a swing shrinks, its half-life, and the energy it loses.

PendulumDamping

Play Big and Fading Swings

Small swings: T₀ = 2π·√(L ÷ g)
Fading: θₙ = θ₀·kⁿ

PLAY NOW · 61

Spring Bounce: Stretch, Bounce, Repeat

A spring pulls back with k·x, and a mass on it bounces with T = 2π·√(m ÷ k). Find a stretch, a period, a spring, a top speed, and a period from the stretch alone.

Simple harmonic motionHooke's law

Play Spring Bounce

Hooke's law: F = k·x
Period: T = 2π·√(m ÷ k)

PLAY NOW · 62

Spring Shop: Side by Side or End to End?

Springs side by side share the load and act stiffer; end to end, each carries it all and they act softer. Predict stretches, the stiffness of half a spring and of a mixed pair, and a bounce.

Hooke's lawSprings combined

Play Spring Shop

Side by side: k = k₁ + k₂
End to end: 1/k = 1/k₁ + 1/k₂

PLAY NOW · 63

Spring Launcher: Push, Store, Release

A squashed spring stores ½·k·x² and hands it on when let go. Launch a pinball and a rocket, aim for a platform, see what doubling the push does, and stop a cart with a spring.

Elastic energyEnergy conservation

Play Spring Launcher

Stored energy: E = ½·k·x²
Launch: v = x·√(k ÷ m)

PLAY NOW · 64

Swing and Resonance: Push at the Right Moment

An oscillator trades motion for stored energy and back, and small pushes in time with it build a big swing. Time a swing's pushes, find speeds and energies, and the bumps that make a car resonate.

Simple harmonic motionResonance

Play Swing and Resonance

Energy: E = ½·k·A²
Resonance: f_push = f₀

Waves

27 games

PLAY NOW · 65

Rope Pulse: What Travels Along a Wave?

A wave carries a shape and energy along, while the rope only moves up and down. Time a pulse, watch a ribbon stay put, read the amplitude, add two pulses that meet, and catch an echo.

What a wave isAmplitude

Play Rope Pulse

Wave speed: v = d ÷ t
Pulses add: y = y₁ + y₂

PLAY NOW · 66

Pebble Ripples: Why Waves Shrink as They Spread

A pebble's ripple shrinks as its ring grows, because the same energy is shared around a longer and longer ring. Find the height far away, the energy per metre, the distance where it drops to 1 cm, and compare a straight wave.

AmplitudeEnergy of a wave

Play Pebble Ripples

Spreading ripple: A ∝ 1 ÷ √r
Energy and height: E ∝ A²

PLAY NOW · 67

Power on a Rope: How Much Energy Does a Wave Carry?

A wave carries energy along a rope to an absorber at the far end. Double the amplitude, double the frequency too, work out the watts, find the swing that keeps the power the same, and try a heavier rope.

AmplitudeWave power

Play Power on a Rope

Power of a wave: P = ½·μ·ω²·A²·v
Squares matter: P ∝ A²·f²

PLAY NOW · 68

Ripple Tank Ruler: Measuring Wavelength

A bar dips into a tank 8 times a second and sends straight ripples along it. Count the gaps between crests, read a photo at half size, find the speed with v = f·λ, slow the ripples over a shallow end, and time them across.

WavelengthMeasuring waves

Play Ripple Tank Ruler

Counting gaps: λ = d ÷ (n − 1)
Wave equation: v = f·λ

PLAY NOW · 69

Wave Machine: Wavelength, Frequency, and Speed

A motor shakes one end of a rope and fills it with waves. Count them to find the wavelength, link it to the frequency with v = f·λ, shake faster, time the period at a bead, and test a bigger amplitude.

WavelengthFrequency and period

Play Wave Machine

Wave equation: v = f·λ
Period: T = 1 ÷ f

PLAY NOW · 70

String Tuner: Frequency and Pitch

A string's note is its frequency, f = v ÷ (2·L). Find the note of a guitar string, halve it for an octave, press it to play another note, tighten it, and time one vibration, with a tuner to check.

FrequencySound and pitch

Play String Tuner

String frequency: f = v ÷ (2·L)
Octave: L ÷ 2 → 2·f

PLAY NOW · 71

Strobe Freeze: Catching a Frequency with Flashes

A strobe lights a moving wave for an instant, again and again. Flash once per cycle and it freezes; a little off and it creeps at f − f_s. Freeze a wave, read its creep, measure a frequency, stop a wheel, and find a speed.

FrequencyStrobe effect

Play Strobe Freeze

Seen frequency: f_seen = f − f_s
Frozen by flashes: f_s = f

PLAY NOW · 72

Surfer's Wait: The Period of a Wave

A surfer waiting in one place rises on every crest that passes, once every period T = λ ÷ v. Time the wait, count waves a minute, find the swell's speed and spacing, and turn the period into a frequency.

PeriodOcean waves

Play Surfer's Wait

Period: T = λ ÷ v
Frequency: f = 1 ÷ T

PLAY NOW · 73

Tide Clock: The Period of the Tides

The sea at a harbour rises and falls with a period of about 12 h 25 min. Time four tides, find the low tide, count highs in a day, see why high tide comes 50 minutes later each day, and find the tide's wavelength.

PeriodTides

Play Tide Clock

Period: T = 12 h 25 min
Wavelength: λ = v·T

PLAY NOW · 74

Rope Tension Lab: How Fast a Wave Runs on a Rope

A pulse on a tight rope runs at v = √(F ÷ μ): faster with more tension, slower on a heavier rope. Find a pulse's speed, see why four times the tension only doubles it, find the tension a speed needs, and time a pulse across a rope.

Wave speedRopes

Play Rope Tension Lab

Speed: v = √(F ÷ μ)
Tension: F = μ·v²

PLAY NOW · 75

Tsunami Race: How Depth Sets a Wave's Speed

A tsunami is so long that the whole depth of the sea moves with it, and its speed is v = √(g·h). Find its speed over a deep ocean, turn it into km/h, time a 2000 km crossing, see it slow near the shore, and read the depth from a speed.

Wave speedTsunamis

Play Tsunami Race

Speed: v = √(g·h)
Depth: h = v² ÷ g

PLAY NOW · 76

Slinky Lab: Transverse and Longitudinal Waves

Shake a slinky side to side and each coil moves across it: a transverse wave. Push and pull it and each coil moves along it, bunching into compressions: a longitudinal wave. Find the angle of a coil's motion, the spacing of compressions, and their speed.

Transverse and longitudinalSlinky

Play Slinky Lab

Wave speed: v = f·λ
Compressions: λ = v ÷ f

PLAY NOW · 77

Earthquake P and S: Two Kinds of Seismic Wave

An earthquake sends a fast longitudinal P wave and a slower transverse S wave. The gap between them tells a station how far away the quake was. Find that distance, the arrival times, the S wave's shake, and its speed.

Transverse and longitudinalEarthquakes

Play Earthquake P and S

Distance: d = Δt ÷ (1/v_S − 1/v_P)
Arrival gap: Δt = d ÷ v_S − d ÷ v_P

PLAY NOW · 78

Echo Sounder: Distances from Echoes

An echo is sound that bounced back, so it travels the distance twice: d = v·t ÷ 2. Sound the sea floor with sonar, find a bat's moth, time a cliff's echo, measure the speed of sound in sea water, and find a shoal of fish.

ReflectionSonar and echoes

Play Echo Sounder

Distance: d = v·t ÷ 2
Echo time: t = 2d ÷ v

PLAY NOW · 79

Bank Shot Ripples: How Waves Reflect

A ripple leaves a wall at the same angle it arrived. A pulse on a rope comes back upside down from a clamped end and upright from a free end. Find the angle out, aim a bank shot, predict each pulse's way up, and time a return trip.

ReflectionRipples and ropes

Play Bank Shot Ripples

Angle out: θ_out = θ_in
Fixed end: y_back = −y

PLAY NOW · 80

Shallow Beach: Waves That Bend

Waves slow down in shallow water. Their frequency stays the same, so their wavelength shrinks, and if they arrive at an angle they bend: refraction. Find the new wavelength, the frequency, the angle, the speed, and the depth over a sandbank.

RefractionSea waves

Play Shallow Beach

Wavelength: λ₂ = λ₁·v₂ ÷ v₁
Snell's law: sin θ₁ ÷ sin θ₂ = v₁ ÷ v₂

PLAY NOW · 81

Spearfishing: Light That Bends in Water

Light is slower in water, so it bends as it crosses the surface: n₁·sin θ₁ = n₂·sin θ₂. A fish looks shallower than it is. Find a fish's real depth, a laser's angle in water, where to aim a spear, a liquid's index, and the critical angle.

RefractionLight

Play Spearfishing

Snell's law: n₁·sin θ₁ = n₂·sin θ₂
Real depth: d = n·d_seen

PLAY NOW · 82

Two Speakers: Loud and Quiet Spots

Two speakers playing the same note fill a room with loud and quiet spots. It is quiet where one is half a wave farther than the other: Δd = (n + ½)·λ. Find quiet and loud spots, a frequency, a wavelength, and what a reversed speaker does.

InterferenceSound

Play Two Speakers

Quiet spots: Δd = (n + ½)·λ
Loud spots: Δd = n·λ

PLAY NOW · 83

Beat Tuner: Notes That Wobble

Two notes close in pitch drift in and out of step, so the sound swells and fades |f₁ − f₂| times a second. Tuners listen for the beats to slow and stop. Find a beat rate, a retuning, the time between beats, sharp or flat, and a pitch gap.

BeatsSound

Play Beat Tuner

Beat frequency: f_b = |f₁ − f₂|
Time between beats: T_b = 1 ÷ f_b

PLAY NOW · 84

Harbour Gap: Waves That Spread

Waves spread out after passing a gap, most when the gap is about one wavelength. Far behind it, the first calm direction is sin θ = λ ÷ a. Find calm directions, the gap that calms a boat, a wavelength, and when waves fill the whole harbour.

DiffractionWater waves

Play Harbour Gap

First calm direction: sin θ = λ ÷ a
Wavelength: λ = v·T

PLAY NOW · 85

Laser Slit: Light That Spreads

Light through a narrow slit spreads into a bright band with dark bands either side. The first dark band is y = λ·L ÷ a from the centre. Find a dark band, the central band's width, a slit's width, a laser's wavelength, and the second dark band.

DiffractionLight

Play Laser Slit

First dark band: y = λ·L ÷ a
Central band: w = 2·λ·L ÷ a

PLAY NOW · 86

Ambulance Pass-by: The Siren's Changing Pitch

A moving siren squeezes its sound waves together ahead and stretches them behind, so you hear it higher as it comes and lower as it goes: f' = f·v ÷ (v ∓ v_s). Find the pitch coming and going, an ambulance's speed, a siren's note, and an octave.

Doppler effectSound

Play Ambulance Pass-by

Coming towards you: f' = f·v ÷ (v − v_s)
Going away: f' = f·v ÷ (v + v_s)

PLAY NOW · 87

Paddling Duck: Ripples Ahead and Behind

Each paddle sends out a ring from where the duck is, so the rings crowd together ahead and spread out behind: λ' = (v ∓ v_s) ÷ f. Faster than its ripples, the duck makes a V-shaped bow wave. Find spacings, a speed, a paddling rate, and a bow wave's angle.

Doppler effectWater waves

Play Paddling Duck

Ripple spacing: λ' = (v ∓ v_s) ÷ f
Bow wave: sin θ = v ÷ v_s

PLAY NOW · 88

Decibel Meter: How Loud Is Loud?

Decibels count powers of ten: L = 10·log(I ÷ I₀), so every 10 dB is ten times the intensity, and twice as far away is about 6 dB quieter. Find the level of ten speakers, the drop with distance, an intensity ratio, a level, and a distance.

SoundDecibels

Play Decibel Meter

Sound level: L = 10·log(I ÷ I₀)
Distance: I ∝ 1 ÷ r²

PLAY NOW · 89

Bottle Flute: Notes from Air and Water

A bottle is a pipe closed at one end: its air column holds a quarter of a wave, so f = v ÷ 4L. Pour in water and the column shortens, so the pitch rises. Find a bottle's note, the note after pouring, a column length, how much to pour, and the next note up.

SoundResonance

Play Bottle Flute

Closed pipe: f = v ÷ 4L
Higher notes: f_n = n·v ÷ 4L

PLAY NOW · 90

Antenna Workshop: How Long Is a Radio Wave?

Radio, Wi-Fi, and microwaves are waves that travel at 3 × 10⁸ m/s. Use λ = c ÷ f to find their wavelengths, size a quarter-wave antenna, space a microwave oven's hot spots, and see why AM masts are so tall.

WavelengthRadio waves

Play Antenna Workshop

Wavelength: λ = c ÷ f
Quarter-wave antenna: L = λ ÷ 4

PLAY NOW · 91

Sound in Slow Motion: A Wave You Can Hear

Sound is a wave of squeezes in the air, travelling at 340 m/s. Slow a note down to see its wavelength and period, then use the speed of sound to find a storm from its thunder and a cliff from its echo.

Sound wavesWavelength and period

Play Sound in Slow Motion

Wavelength: λ = v ÷ f
Distance: d = v·t

Electrostatics

10 games

PLAY NOW · 92

Static Rub: Charge from Moving Electrons

Rubbing doesn't make charge; it moves electrons: Q = −n·e on one side, +n·e on the other. Charge a balloon, see what the wool keeps, count electrons, and make an ion.

Electric chargeElectrons

Play Static Rub

Charge: Q = −n·e
Electrons: n = |Q| ÷ e

PLAY NOW · 93

Oil Drop: Charge Comes in Electrons

A charged drop hovers when the electric force balances its weight: q·V ÷ d = m·g. Measure charges, count electrons, set the voltage, and find e from three drops.

Electric chargeMillikan's experiment

Play Oil Drop

Hovering: q·V ÷ d = m·g
Electrons: q = n·e

PLAY NOW · 95

Material Tester: Conductors and Insulators

A material's resistivity decides whether it conducts: R = ρ·L ÷ A, I = V ÷ R. Copper and glass are twenty powers of ten apart. Test five samples on a 12 V bench.

ConductorsResistivity

Play Material Tester

Resistance: R = ρ·L ÷ A
Current: I = V ÷ R

PLAY NOW · 96

Floating Bead: Coulomb's Law Against Gravity

Like charges push apart with F = k·q₁·q₂ ÷ r², harder the closer they are. A bead floats where that push equals its weight. Find the gap, the charge, the mass, and the floor's push.

Coulomb's lawElectric force

Play Floating Bead

Floating: k·q₁·q₂ ÷ r² = m·g
Gap: r = √(k·q₁·q₂ ÷ m·g)

PLAY NOW · 97

Charge Tug: Forces Between Charges

Charges push or pull with F = k·q₁·q₂ ÷ r², equal and opposite, and forces from several charges add. Measure a pull, find a balance point, add two forces, find a charge, and double everything.

Coulomb's lawAdding forces

Play Charge Tug

Two charges: F = k·q₁·q₂ ÷ r²
Balance point: q₁ ÷ x² = q₂ ÷ (d − x)²

PLAY NOW · 98

Field Probe: Force per Charge

The electric field is the force on a test charge divided by its charge, E = F ÷ q, and a point charge makes E = k·Q ÷ r². Find a field from a force, size a probe's force, add two fields, and find a distance.

Electric fieldForce per charge

Play Field Probe

Field from a force: E = F ÷ q
Field of a point charge: E = k·Q ÷ r²

PLAY NOW · 99

Electron Beam: Bending Charges with a Field

Between two charged plates the field is uniform, E = V ÷ d, and a charge feels a steady push across the beam, so its path bends into a parabola. Find the field, the acceleration, the bend, the voltage for a target, and a proton's bend.

Uniform fieldCharged particles

Play Electron Beam

Field between plates: E = V ÷ d
Bend in the plates: y = ½·(q·E ÷ m)·(L ÷ v₀)²

PLAY NOW · 100

Potential Map: Energy per Charge

Electric potential is energy per charge: a point charge makes V = k·Q ÷ r, potentials add as plain numbers, and carrying a charge q takes work W = q·ΔV. Read a potential, climb, walk a contour, add two charges, and find a ring.

Electric potentialWork and energy

Play Potential Map

Potential of a charge: V = k·Q ÷ r
Work to carry a charge: W = q·ΔV

PLAY NOW · 101

Particle Gun: Voltage into Speed

A charge that falls through a potential difference ΔV gains kinetic energy q·ΔV = ½·m·v². Find an electron's energy and speed, a proton's speed, an alpha particle's energy in eV, and the voltage that stops an electron.

Potential differenceKinetic energy

Play Particle Gun

Energy gained: K = q·ΔV
Speed reached: v = √(2·q·ΔV ÷ m)

Electric circuits

16 games

PLAY NOW · 102

Battery Stack: Adding Up Voltages

Cells in a row add their voltages, a flipped cell takes its voltage away, and cells side by side give the voltage of one. A battery gives every coulomb it moves V joules: W = Q·V. Stack, flip, line up, power a lamp, and count cells.

VoltageCells in series

Play Battery Stack

Cells in a row: V = V₁ + V₂ + …
Energy per charge: W = Q·V

PLAY NOW · 103

Voltmeter Walk: Voltage Between Two Points

A voltmeter reads the potential at its red probe minus the potential at its black probe: V = V_red − V_black. Swap the probes, try an open switch and a plain wire, find the voltage at a junction, and set two cells against each other.

VoltageUsing a voltmeter

Play Voltmeter Walk

A voltmeter reads: V = V_red − V_black
Down a resistor: ΔV = I·R

PLAY NOW · 104

Charge Gate: Current Is Charge per Second

A current is the charge that passes a cut across the wire each second: I = Q ÷ t, and one ampere is one coulomb a second, about 6 × 10¹⁸ electrons. Count the charge at the gate, turn minutes and hours into seconds, and time a slow current.

CurrentCharge and time

Play Charge Gate

Current is: I = Q ÷ t
One ampere: 1 A = 1 C/s

PLAY NOW · 105

Snail Electrons: Slow Drift, Fast Signal

Electrons jitter at about a million metres a second but drift along a wire like snails: I = n·e·A·v_d gives under a tenth of a millimetre a second for 1 A in copper. Yet a lamp lights at once, because the signal runs along the wire at 2 × 10⁸ m/s.

CurrentDrift speed

Play Snail Electrons

Current from drift: I = n·e·A·v_d
The signal: v ≈ 2 × 10⁸ m/s

PLAY NOW · 106

Wire Stretcher: Length and Thickness Set Resistance

A wire's resistance grows with its length and falls with its cross-section: R = ρ·L ÷ A. Twice the length doubles R, twice the diameter gives a quarter, and stretching a wire to twice its length makes R four times larger. Unroll, stretch, and cut a coil to size.

ResistanceResistivity

Play Wire Stretcher

Resistance of a wire: R = ρ·L ÷ A
Round wire: A = π·d² ÷ 4

PLAY NOW · 107

Hot Filament: Resistance Rises with Temperature

A metal resists more as it heats: R = R₀·(1 + α·(T − T₀)). A lamp filament at 2500 °C has twelve times its cold resistance, so a lamp takes a surge of current when switched on, and a platinum wire makes a thermometer. Heat, glow, and read the temperature.

ResistanceTemperature

Play Hot Filament

Hot resistance: R = R₀·(1 + α·ΔT)
Platinum sensor: R = 100 Ω·(1 + 0.00385·T)

PLAY NOW · 108

Ohm's Law Lab: Current, Voltage, and Resistance

For a fixed resistor, the current grows in proportion to the voltage: V = I·R, a straight line through the origin on an I–V graph. Find a current, a resistance, or a voltage from the other two, read a line, and pick the resistor that keeps an LED at 20 mA.

Ohm's lawI–V graph

Play Ohm's Law Lab

Ohm's law: V = I·R
Rearranged: I = V ÷ R, R = V ÷ I

PLAY NOW · 109

Fuse Test: Ohm's Law Meets Its Limits

I = V ÷ R sets every current here, and a fuse melts the moment the current reaches its rating. Find a kettle's current, the smallest resistance a fuse survives, why a fuse does not protect a person, the most voltage a resistor can take, and the huge current of a short circuit.

Ohm's lawFuses

Play Fuse Test

Current: I = V ÷ R
The fuse melts when: I ≥ I_fuse

PLAY NOW · 110

Bulb Chain: One Path for Every Bulb

In a series circuit there is only one path, so the same current flows through every bulb and the resistances add: R = R₁ + R₂ + …. Find the current, the total resistance, one bulb's share of the voltage, why a fourth bulb dims them all, and how many fairy lights the mains needs.

Series circuitsVoltage sharing

Play Bulb Chain

Resistances add: R = R₁ + R₂ + …
Same current: I₁ = I₂ = I₃

PLAY NOW · 111

Voltage Divider: Sharing the Supply

Two resistors in series split the supply in proportion to their resistances: V_out = V·R₂ ÷ (R₁ + R₂). Find an output voltage, design a divider for 5 V, read a light sensor and a thermistor, and find the voltage partway down a chain of three.

Voltage dividersSensors

Play Voltage Divider

Output: V_out = V·R₂ ÷ (R₁ + R₂)
Shares in proportion: V₁ ÷ V₂ = R₁ ÷ R₂

PLAY NOW · 112

Room Wiring: Every Branch Gets the Full Voltage

Parallel branches each get the full voltage: the currents add and the combined resistance falls, 1/R = 1/R₁ + 1/R₂ + …. Find a combined resistance and a main current, see why the other lamps stay lit when one is unplugged, choose a resistor, and count the lamps a breaker allows.

Parallel circuitsHouse wiring

Play Room Wiring

Resistance: 1/R = 1/R₁ + 1/R₂ + …
Main current: I = I₁ + I₂ + …

PLAY NOW · 113

Current Splitter: What Flows In Flows Out

Current is never used up at a junction: what flows in flows out, I = I₁ + I₂ + …. Branches in parallel share one voltage, so the smaller resistance takes the larger share. Find a missing current, divide a current, add the branches, see why a new branch leaves the old one alone, and design a shunt.

Kirchhoff's current lawCurrent division

Play Current Splitter

At a junction: I_in = I_out
Same voltage: I₁·R₁ = I₂·R₂

PLAY NOW · 114

Bulb Brightness: Power, Not the Label

Power is the rate a bulb turns electrical energy into light and heat: P = V·I = I²·R = V² ÷ R. Its rating only fixes its resistance. Find a power, a bulb's resistance, what two bulbs in series give, why the 60 W bulb wins when paired with a 100 W one, and what half the voltage does.

Electrical powerRatings

Play Bulb Brightness

Power: P = V·I = I²·R = V² ÷ R
From a rating: R = V² ÷ P

PLAY NOW · 115

Power Line: Why the Wires Run at High Voltage

The same power can be sent as a large current at low voltage or a small current at high voltage, and the line's heating grows with the current squared: P_loss = I²·R. Find the loss at two voltages, design a line that loses 1%, heat a line, and size a heater at the house.

Electrical powerTransmission lines

Play Power Line

Line current: I = P ÷ V
Line loss: P_loss = I²·R

PLAY NOW · 116

Kettle Race: Energy Is Power Times Time

The energy a kettle supplies is its power times the time, E = P·t, and the water needs m·c·ΔT to warm up. Race a kettle against your predicted time, find the energy it uses, see what heat losses do, choose a power, and see why a kettle abroad takes four times as long.

Electrical energyHeating water

Play Kettle Race

Energy: E = P·t
Heating water: E = m·c·ΔT

PLAY NOW · 117

Energy Meter: The Kilowatt-Hour Is an Energy

The kilowatt-hour on an energy bill is not a power but an energy: 1 kW for 1 h, or 3600 kJ. Find a lamp's energy, what standby costs in a month, a power bank in kilojoules, what an LED saves over 1000 hours, and how much energy a phone battery holds.

Electrical energyKilowatt-hours

Play Energy Meter

Energy: E (kWh) = P (kW) · t (h)
Conversions: 1 kWh = 3600 kJ

Educational simulation games that turn questions into experiments

Use Phisicos to explore one idea at a time. Each educational simulation game pairs a controllable physics model with a challenge: chase a ghost to connect distance, time, and direction, or land a module by balancing gravity and thrust.

Predict how the motion will unfold.
Play, pause, or advance by 0.10 seconds.
Compare the measurements and explain the result.

Educational simulation gamesfor learning physics.

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Educational simulation games

Educational simulation games
for learning physics.